The present invention relates to a novel structure for column supported concrete slabs in accordance with the preamble to the attached Claim 1 and to a method for making such structures in accordance with the preamble to the attached Claim 5.
The flat plate is a very common and commercially competitive structural system for cast-in-place slabs in buildings, since no beams, column capitals or drop panels, i.e. thickened portions around columns, are involved, thus making the formwork extremely simple. The structural concept is at a great disadvantage, however, because of the risk of brittle punching failure at the slab-column connection. Extensive research efforts have therefore been devotedxe2x80x94and are still being devotedxe2x80x94to the development of methods for reliably predicting punching shear capacity.
Modern building codes require that a structure be designed in such a way xe2x80x9cthat it will not be damaged by events like explosions, impact or consequences of human errors, to an extent disproportionate to the original causexe2x80x9d. (European Committee for Standardization, Eurocode 2, Design of Concrete Structures, Part 1: General Rules and Rules for Buildings, ENV 1992-1-1:1991). In other words: a local failure must not lead to progressive collapse of the entire structure. Attention has been directed to fulfilling this requirement in the case of flat plates, i.e. preventing a punching failure at one column, due to a gas explosion for example, from leading to subsequent punching at adjacent columns due to large slab rotations, and possible progressive collapse.
These problems and possible solutions were addressed in several scientific publications by the present inventor: Broms, Carl Erik, xe2x80x9cPunching of Flat Platesxe2x80x94A Question of Concrete Properties in Biaxial Compression and Size Effectxe2x80x9d, ACI Structural Journal, V. 87, No. 3, May-June 1990, pp. 292-304 and xe2x80x9cShear Reinforcement for Deflection Ductility of Flat Plates,xe2x80x9d ACI Structural Journal, V. 87, No. 6, November-December 1990, pp. 696-705. In this latter article, it was pointed out the necessity of designing and arranging the reinforcement for flat plates so that a ductile failure mode is guaranteed. To achieve this, the article proposed the use of inter alia two pairs of bent bars laid at right angles to each other over the column end. The bent bars follow a bottom flexural reinforcement net adjacent the bottom surface of the flat plate, except at the columns where they slant upwards and follow the top flexural reinforcement net adjacent the top surface of the flat plate. The solution suggested in the latter ACI Structural Journal article also incorporates a stirrup cage unit, comprising several rows of U-shaped spaced bars, connected by longitudinally extending parallel bars. This previously known stirrup cage unit is shown in FIG. 8. The bottom flexural reinforcement net is placed on top of the stirrup cage arrangement, which is placed in the form first. This locks the stirrup cage arrangement in place in accordance with established practice. The bent bars are then put in place, whereupon the top flexural reinforcement net is put in place and the concrete is poured.
Solutions for preventing punching shear must come from an understanding of the basic principles of the failure mechanism.
Most concrete codes define the punching capacity in terms of nominal shear stress acting on a vertical surface a certain distance away from the column. That approach is unfortunate since it incorrectly implies that the punching capacity is governed by the diagonal tensile strength of the concrete slab. In fact diagonal cracks normally develop already at a load level on the order of xc2xd to ⅔ of the ultimate load. These cracks can completely surround the column, the slab is still stable and can be unloaded and reloaded several times at that load level without any decrease of the ultimate capacity.
The punching failure occurs instead when the concrete in compression at the bottom of the slab near the column is distressed by the high tangential xe2x80x9csqueezingxe2x80x9d due to the global flexural curvature. At columns with small diameter, the inclined compression stress in the radial direction below the shear crack may govern.
The failure mechanism described above clarifies why stirrups or stud rails generally do not result in the desired ductile behavior. For such shear reinforcement, a capacity increasexe2x80x94as well as some ductility increasexe2x80x94is normally encountered in relation to a flat plate without shear reinforcement, but the failure mode is still a sudden punching failure.
If the stirrups or studs extend far enough from the column to prevent a shear failure outside the shear reinforcement, typically a steep shear crack forms near the column passing between the stirrups (studs) at failure. This occurs because the distressed compressed concrete near the column becomes too soft when the tangential strain reaches a critical levelxe2x80x94a scenario that differs from beams and one-way slabs where tangential compression does not occur.
The detrimental effect on the tensile capacity of the concrete in perpendicular direction to the tangential compression is demonstrated if the shear reinforcement is not extended far enough from the column. Then a diagonal tension failure will ultimately develop outside the shear reinforcement. Once the diagonal crack opens up it will immediately propagate within the soft concrete cover under the shear reinforcement all the way up to the column.
The solution presented in the latter ACI Structural Journal article discussed above, has however not been readily adopted by builders despite advantages shown, due to the extra steps involved in interlacing the bottom reinforcement net on top of the trough bottoms of the stirrup cage unit, thereby anchoring the stirrup cage unit in place in accordance with accepted practice.
One proposed method is described inter alia in U.S. Pat. No. 4 406 103 (Ghali et al.) which deals with the reinforcement of concrete slabs in the vicinity of columns and suggests the use of a line of spaced vertical members in the form of thin I-beam sections or rods welded to a base or horizontal longitudinal rod. These proposed means are difficult, time-consuming and thus costly to construct. They do not provide the ductility required to prevent punching under extreme loads, as dictated by the analysis above.
Prevailing knowledge, including the US patent referred to above, has dictated that the bottom flexural reinforcement net must be placed on top of parts of the stirrup cages to anchor them. This has made the implementation of the solutions proposed in the present inventor""s November-December 1990 article in ACI Structural Journal (discussed above) more difficult.
These problems are solved by a concrete flat slab structure supported horizontally on at least one substantially vertical column, said slab structure having a body of cast concrete with a bottom surface and a top surface opposite thereto, a bottom flexural reinforcement net embedded in said body adjacent the bottom surface, a top flexural reinforcement net embedded in said body adjacent the top surface, and, in an area immediately surrounding each column, a stirrup cage arrangement made up of vertically oriented U-shaped bars interconnected in spaced relationship by longitudinally extending horizontal bars, as well as two or more bent bars laid substantially at right angles to each other over the column end, each of said bent bars running substantially along said bottom flexural reinforcement net except at the columns where the bent bars run substantially along said top flexural reinforcement net, characterized in that the longitudinally extending horizontal bars of the stirrup cage arrangement are disposed in a non-interlocking manner on top of the bottom flexural reinforcement net and that said top flexural reinforcement net is disposed in a non-interlocking manner on top of the stirrup cage arrangement; and by a method of building a concrete slab structure supported horizontally on at least one substantially vertical column, said method comprising the following steps of:
a. laying in a form a bottom flexural reinforcement net;
b. placing, in areas adjacent each column on either side thereof, in parallel rows, long stirrup cages, each composed of a series of vertically oriented U-shaped bars connected, in spaced relationship with each other, by two longitudinally extending bars fixed to the ends of the legs of each U-shaped bar;
c. laying, at right angles to each other and crossing each other at the respective column, at least two bent bars, in such a way that each of said bars runs substantially along said bottom flexural reinforcement except at the columns;
d. laying, on top of said stirrup cages and said bent bars, a top flexural reinforcement net;
e. pouring concrete in said form to a level above said top flexural reinforcement net and allowing it to set.